after a particularly cold night, Alice leaves a tub of water outside. You may consider the ground and air to have temperatures of Tc = −10 °C and Th = 10 °C respectively. How thick is the layer of ice that forms at the bottom of the tub of water, after the tub has been left outside for a long time? The tub of water initially has a layer of water of thickness h0 = 10 cm. You may assume that the ground and air remain at a constant temperature throughout, and that the side lengths of the tub a, b ≫ h0, i.e. the heat conduction is one- dimensional. Density of ice and water are ρice = 920 kg/m^3 and ρw = 1000 kg/m^3 . Ice and water have thermal conductivities of kice = 2.22 W K^-1 m^−1 and kw = 0.556 W K^−1 m^−1
after a particularly cold night, Alice leaves a tub of water outside. You may consider
the ground and air to have temperatures of Tc = −10 °C and Th = 10 °C respectively. How
thick is the layer of ice that forms at the bottom of the tub of water, after the tub has been
left outside for a long time? The tub of water initially has a layer of water of thickness
h0 = 10 cm. You may assume that the ground and air remain at a constant temperature
throughout, and that the side lengths of the tub a, b ≫ h0, i.e. the heat conduction is one-
dimensional. Density of ice and water are ρice = 920 kg/m^3
and ρw = 1000 kg/m^3 . Ice and
water have thermal conductivities of kice = 2.22 W K^-1 m^−1
and kw = 0.556 W K^−1 m^−1
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